What’s that all about the contrasts

Hi Wolfgang and Michel, here is a simple example to show the differences between treatment and effect contrast.

Example dataset

Create a random dataset with criteria y, predictors x1 and x2 and gender.

All variables are correlated.

n <- 10000
gender <- rep(0:1, each = n/2)
y <- sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x1 <- y + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x2 <- y + x1 + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)

dat <- data.frame(y = y, x1 = x1, x2 = x2, gender = gender)

Descriptives

psych::corr.test(dat)

Call:psych::corr.test(x = dat)
Correlation matrix 
          y   x1   x2 gender
y      1.00 0.80 0.87   0.55
x1     0.80 1.00 0.93   0.67
x2     0.87 0.93 1.00   0.73
gender 0.55 0.67 0.73   1.00
Sample Size 
[1] 10000
Probability values (Entries above the diagonal are adjusted for multiple tests.) 
       y x1 x2 gender
y      0  0  0      0
x1     0  0  0      0
x2     0  0  0      0
gender 0  0  0      0

 To see confidence intervals of the correlations, print with the short=FALSE option

psych::describe(dat)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
y	1	10000	7.5041	4.597858	7.0	7.28475	4.4478	0	20	20	0.3712705	-0.4346202	0.0459786
x1	2	10000	14.9931	7.376659	14.0	14.68075	7.4130	0	39	39	0.3635167	-0.4501117	0.0737666
x2	3	10000	30.0624	13.784706	29.0	29.49638	14.8260	0	76	76	0.3493704	-0.5603446	0.1378471
gender	4	10000	0.5000	0.500025	0.5	0.50000	0.7413	0	1	1	0.0000000	-2.0002000	0.0050003

Contrasts

The left part of the table is with gender as treatment contrast (0 vs. 1) and the right part with gender as effect contrast (-1 vs. 1)

# Gender has values 0 vs. 1 (treatment contrast)
fit1 <- lm(y ~ gender * x1 * x2, data = dat)

# Gender hast -1 vs. 1 (effect contrast)
dat$gender <- car::recode(dat$gender, "0 = -1; 1 = 1")

fit2 <- lm(y ~ gender * x1 * x2, data = dat)

sjPlot::tab_model(fit1, fit2, show.std = TRUE, show.ci = FALSE, col.order = c("est", "se", "std.est", "p"), digits = 4)

	y			y
Predictors	Estimates	std. Beta	p	Estimates	std. Beta	p
(Intercept)	-1.6773	0.0029	<0.001	-2.4592	0.0029	<0.001
gender	-1.5638	-0.1739	<0.001	-0.7819	-0.1739	<0.001
x1	0.0011	-0.0173	0.960	-0.0094	-0.0173	0.507
x2	0.3324	1.0089	<0.001	0.3373	1.0089	<0.001
gender × x1	-0.0209	-0.0176	0.458	-0.0105	-0.0176	0.458
gender × x2	0.0098	0.0139	0.511	0.0049	0.0139	0.511
x1 × x2	-0.0000	-0.0011	0.971	-0.0000	-0.0011	0.915
(gender × x1) × x2	-0.0000	-0.0004	0.968	-0.0000	-0.0004	0.968
Observations	10000			10000
R2 / R2 adjusted	0.763 / 0.763			0.763 / 0.763